[Math] Tree with $k$ edges is a subgraph of any graph with all vertices of degree $\geq k$.

Question

Let $T$ be a tree with $k$ edges. Let $G$ be a graph where every vertex has a degree of at least $k$. Show that $T$ is a subgraph $G$.

I know this implies that in a graph where every vertex is at least $k$, you can find a copy of every tree with $k$ edges, but I'm stuck here.

Answer 1

Hint: Induction on $k$ (deleting a leaf to apply the induction hypothesis).